
theorem Th44:
for G, H being SimpleGraph
 st G c= H holds G c= H SubgraphInducedBy Vertices G
proof
  let G, H be SimpleGraph;
  assume A1: G c= H;
  set L = Vertices G;
  let g be object;
  reconsider gg=g as set by TARSKI:1;
  assume A2: g in G;
      gg c= Vertices G by A2,ZFMISC_1:74;
  hence g in H SubgraphInducedBy L by A2,A1,XBOOLE_0:def 4;
end;
